Publication

Publications:

  1.  The Navier-Stokes equations on manifolds with boundary. J. Differential Equations 416, part 2, 1602-1659 (2025). (With Gieri Simonett and Mathias Wilke).
  2. Modeling and analysis of ensemble average solvation energy and solute-solvent interfacial fluctuations. Comput. Math. Biophys. 12 (2024), Paper No. 20240017. (With Zhan Chen and Shan Zhao).
  3. A p-Laplacian approach and its analysis for the calculation of ensemble average solvation energy. Communications in Information & Systems 24(3), 275-311 (2024). (With Zhan Chen and Shan Zhao).
  4. Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics. To appear in Asymptomatic Analysis. arXiv:2308.09851 (With Marcelo Disconzi).
  5. On a thermodynamically consistent model for magnetoviscoelastic fluids in 3D. J. Evol. Equ. 24, no. 1, Paper no. 9 (2024). (With Hengrong Du and Gieri Simonett).
  6. A new approach to constrained total variation solvation models and the study of solute-solvent interface profiles. Comput. Math. Appl. 130, 119-136 (2023). (With Zhan Chen).
  7. Well-posedness for magnetoviscoelastic fluids in 3D. Nonlinear Anal. Real World Appl. 69 (2023), Paper No. 103759. (With Hengrong Du and Gieri Simonett).
  8. Convergence of a diffuse interface Poisson-Boltzmann (PB) model to the sharp interface PB model: a unified regularization formulation. Appl. Math. Comput. 436, Paper No. 127501 (2023). (With Mark McMGowon, Siwen Wang, Emil Alexov and Shan Zhao).
  9. The fractional porous medium equation on manifolds with conical singularities II. Mathematische Nachrichten. 296, no. 4, 1616-1650 (2023). (With Nikolaos Roidos).
  10. A regularization approach for solving the super-Gaussian Poisson-Boltzmann model with heterogeneous dielectric functions. J. Comput. Phys. 464, Paper No. 111340, 23 pp. (2022). (With Siwen Wang, Emil Alexov and Shan Zhao).
  11. A constrained variational model of biomolecular solvation and its numerical implementation.  Comput. Math. Appl. 107, 17-28 (2022) (With Zhan Chen, Elizabeth Hawkins and Kai Wang).
  12. Maximal Lq-regularity of nonlocal parabolic equations in higher order Bessel potential spaces. Pure Appl. Funct. Anal. 7, no. 3, 1037-1063 (2022). (With Nikolaos Roidos).
  13. The fractional porous medium equation on manifolds with conical singularities I. J. Evol. Equ. 22, no. 1, Paper No. 8, 39 pp (2022) (With Nikolaos Roidos).
  14. Functional inequalities involving nonlocal operators on complete Riemannian manifolds and their applications to the fractional porous medium equation. Evol. Equ. Control Theory 11, no. 3, ​793-825 (2022). (With Nikolaos Roidos).
  15. Local well-posedness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics. Commun. Pure Appl. Anal. 20, no. 6, 2279-2290  (2021). (With Fabio S. Bemfica, Marcelo M. Disconzi and Casey Rodriguez).
  16. New Variational Analysis on the Sharp Interface of Multiscale Implicit Solvation: General Expressions and Applications. Communications in Information & Systems.  21, no. 1, 37-64 (2021). (With Zhan Chen and Elizabeth Hawkins).
  17. The surface diffusion and the Willmore flow for uniformly regular hypersurfaces. Discrete Contin. Dyn. Syst. Ser. S. 13, no. 12, 3503-3524 (2020). (With Jeremy LeCrone and Gieri Simonett).
  18. Harmonic map heat flow on conic manifolds. Accepted by Contemporary Mathematics. Nonlinear Dispersive Waves and Fluids, 227–250, Contemp. Math., 725, Amer. Math. Soc., Providence, RI, 2019. (With Changyou Wang).
  19. The Yamabe flow on incomplete manifolds. J. Evol. Equ. 18, no. 4, 1595–1632 (2018).
  20. Wellposedness of a nonlocal nonlinear diffusion equation in image processing. Nonlinear Anal. 150, 114-137 (2017). (With Patrick Guidotti).
  21. Continuous maximal regularity on manifolds with singularities and its applications. Evol. Equ. and Control Theory 5, no. 2, 303-335 (2016).
  22. Singular parabolic equations of second order on manifolds with singularities. J. Differential Equations 260, no. 2, 1747-1800 (2016).
  23. On the regularity of the interface of a thermodynamically consistent two-phase Stefan problem. Interfaces Free Bound. 17, no. 4, 555–600 (2015). (With Jan Prüss, and Gieri Simonett).
  24. Some remarks on uniformly regular Riemannian manifolds. Math. Nachr. 289, No. 2-3, 232-242 (2016). (With Marcelo Disconzi, and Gieri Simonett).
  25. A family of parameter-dependent diffeomorphisms acting on function spaces over a Riemannian manifold and applications to geometric flows. NoDEA Nonlinear Differential Equations Appl. 22, no. 1, 45-85 (2015).
  26. Continuous maximal regularity on uniformly regular Riemannian manifolds. J. Evol. Equ. 1, no. 14, 211-248 (2014). (With Gieri Simonett).
  27. Real analytic solutions to the Willmore flow. Ninth MSU-UAB Conference on Differential Equations and Computational Simulations; Electron. J. Diff. Eqns., Conf. 20, pp. 151-164 (2013).

Preprints:

  1. Degenerate parabolic p-Laplacian equations: existence, uniqueness and asymptotic behavior of solutions. arXiv:2405.13849 (With David Cruz-Uribe, OFS, and Kabe Moen).
  2. Coriolis-driven fluid motion on spherical surfaces. arXiv:2412.20187v1 (With Gieri Simonett and Mathias Wilke).